Soliton solutions of the nonlinear Schrödinger equation with nonlocal Coulomb and Yukawa interactions

We study the nonlinear Schrödinger equation in (1+1)(1+1) dimensions in which the nonlinear term is taken in the form of a nonlocal interaction of the Coulomb or Yukawa-type. We solve the equation numerically and find that, for all values of the nonlocal coupling constant, and in all cases, the equation possesses solitonic solutions. We show that our results, for the dependence of the height of the soliton on the coupling constant, are in good agreement with the predictions based on an analytic treatment in which the soliton is approximated by a Gaussian.